# Integral representation of a generic function

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 July 5, 2012, 03:23 Integral representation of a generic function #1 New Member   ali Join Date: Apr 2010 Posts: 3 Rep Power: 7 Hey guys, I've just started reading SPH book by Liu & Liu. In second chapter, I faced with an expression which says the integral representation of a generic function is: f(x)=int[f(x')*DeltaDirac(x-x')*dx'] I cannot understand the concept behind this formulation. Could anyone someone please help me to get through it? you know, this is somehow none-sense for me, when x'-->x then we are going to have something like this: {f(x)=int[f(x')*1*dx'] where x=x'} so it means that {f(x)=int[f(x)*dx]}!!!! Please correct me if I am wrong, I do appreciate your help.

July 5, 2012, 04:25
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Filippo Maria Denaro
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Quote:
 Originally Posted by gentela Hey guys, I've just started reading SPH book by Liu & Liu. In second chapter, I faced with an expression which says the integral representation of a generic function is: f(x)=int[f(x')*DeltaDirac(x-x')*dx'] I cannot understand the concept behind this formulation. Could anyone someone please help me to get through it? you know, this is somehow none-sense for me, when x'-->x then we are going to have something like this: {f(x)=int[f(x')*1*dx'] where x=x'} so it means that {f(x)=int[f(x)*dx]}!!!! Please correct me if I am wrong, I do appreciate your help.

No, Dirac(0) goes to infinity, is its integral to be finished and =1. That defines the function f at a position x

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